Hi again Mike,
In fairness, I have to say that when it's intended primarily for highway cruising use with a moderately tuned engine the J-type will probably do fine. Some points in its favor are that in stock form it will typically have a little more reduction (25% compared to 22%), most likely you will only be using it on top gear (where it's least stressed and OD durability is less of a concern) and you won't object to a slight delay as it engages.
That's a bit different than using the OD as a sort of "7-speed" gearbox. I.e. using the OD on 2nd and 3rd, as well as top gear to get just the right rpms in fast corners. For a more "sporting" purpose like this, an A-type might be preferred.
So, if you can get a J-type cheap, it might work out really well. Just so you know, a key reason J-type takes longer to engage than an A-type is that the A-type runs at high pressure all the time, while the J-type doesn't build up to engagement pressure until the switch is turned on. The A-type uses a higher overall pressure, too. Because of this, the A-type is a little more inclined to leak oil than the J-type.
Some other things to consider. Yes, the gearbox will still need to be modified with a shorter main shaft. It should also at a very minumum be thoroughly cleaned inside. Any used OD should at least be cleaned carefully, too. This is because the two share oil and one that's in rough shape can contaminate and damage the other. You are also correct that an adapter plate is also needed, between the gearbox and the OD. I'm not sure if the one for the J-type is different from the A-type adapter plate, but would guess it is. The electrical harness, switch and relay are all pretty easy to find or make up, so really aren't an issue.
Now, Volvo has shared a lot of parts with Triumph over the years. So, by all means there is good likelihood a Volvo OD, specifically, can be made to work. Often the major difference between Laycock OD units is the tail piece, providing different mounting methods for different cars and, often, differing speedo drive fittings and gear ratios. Even so, a fabricated adapter plate might work if the rear mounting is different, instead of trying to track down a tailpiece for the OD. And, often an angle drive can be used on the speedo fitting to resolve clearance issues, but doesn't correct for any gearing differences that would make your speedometer inaccurate. However, the speedo drive in the OD might be changeable, or the speedometer itself might be re-calibrated instead.
All are certainly issues that can be resolved. It would be great, though, to work with someone who probably has some expertise on making this sort of swap, like John Esposito at Quantum Mechanics.
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